Generalized coordinate transformation and gas-kinetic scheme

Under a generalized coordinate transformation with inclusion of both mesh velocity and acceleration, the gas-kinetic equation is transformed from a physical space to a computational space. With the WENO reconstruction, a high-order moving-mesh multidimensional gas-kinetic method, with inclusion of both normal and tangential derivatives of macroscopic flow variables, is constructed. High-order accurate Navier-Stokes solutions are obtained in the current scheme by integrating the numerical fluxes along a cell interface and over a whole time step, without using the conventional Gaussian point integration for spatial accuracy and Runge-Kutta method for temporal accuracy. For the first time, the mesh acceleration has been explicitly accounted for in the flux evaluation. Under the generalized coordinate transformation, a three-dimensional moving-mesh gas-kinetic scheme has been constructed as well. The importance of multi-dimensionality in the flux evaluation and mesh movement is illustrated through numerical tests.